Archimedes - Cone Quotes

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First then I will set out the very first theorem which became known to me by means of mechanics, namely that
Any segment of a section of a right angled cone (i. e., a parabola) is four-thirds of the triangle which has the same base and equal height,
and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]...

Archimedes

Any segment of a right-angled conoid (i. e., a paraboloid of revolution) cut off by a plane at right angles to the axis is 1½ times the cone which has the same base and the same axis as the segment

Archimedes

The centre of gravity of any cone is [the point which divides its axis so that] the portion [adjacent to the vertex is] triple [of the portion adjacent to the base].

Archimedes